[tex]\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ 1}}\quad ,&{{ \frac{1}{2}}})\quad
% (c,d)
&({{ -1}}\quad ,&{{ -1}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{-1-\frac{1}{2}}{-1-1}\implies \cfrac{\frac{-3}{2}}{-2}
\\\\\\
\cfrac{\frac{-3}{2}}{\frac{-2}{1}}\implies \cfrac{-3}{2}\cdot \cfrac{1}{-2}\implies \cfrac{3}{4}[/tex]
[tex]\bf y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-\cfrac{1}{2}=\cfrac{3}{4}(x-1)\\
\left. \qquad \right. \uparrow\\
\textit{point-slope form}
\\\\\\
y-\cfrac{1}{2}=\cfrac{3}{4}x-\cfrac{3}{4}\implies y=\cfrac{3}{4}x-\cfrac{3}{4}+\cfrac{1}{2}\implies y=\cfrac{3}{4}x-\cfrac{1}{4}[/tex]
